you can use Motorcycle semi synthetic oils, or full synthetic oils too, just make sure they are ok for bikes with wet clutch's
the oil filter in most 125's like the Lifan etc, is just a mesh strainer, it is located behind the r/h clutch/engine cover, towards the front at the bottom, directly above the oil drain bolt.
you need to remove the kick start lever, then the cover retaining bolts and slide the cover off carefully so you don't break the gasket.
once you have the cover off you should see the strainer
Page 16, section E9 part number 14 here
no you don't have to, it just prolongs the life of your engine.
they don't need to be changed, just cleaned with petrol/degreaser and refitted.
if it has never been cleaned it can be holding metal shavings and possibly other stuff too (rubber, gearbox teeth etc)
if it is blocked up, it can cause your oil pump to fail, or no oil circulation to you head, valves and bearings etc etc.
this is a filter screen from a bike i serviced a couple of months ago.
this is what it started out looking like when it was new
that could be the right set, but it may not too.
you need to pull the engnie apart and measure it all up first.
it could also be the shift drum, or shift forks, or it might be a loose bolt holding the shift drum in too.
nah you should be fine,
just be careful when you take it off so you don't break the gasket.
otherwise you might need some silicon to fix it .
it is just the side cover, not really opening up the engine.